Finite Group Databasebeta

← C4×#88132 #13117367

Subgroups — C4×#88132 #13117367

Order 1664.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic13C211yesmaximal, characteristic
2C2×#88132C211yesmaximal, characteristic
3C2×C4×Dic26C211yesmaximal, characteristic, complemented
4C4×C13×C22⋊C4C211yesmaximal, characteristic
5C4×C22⋊Dic13C211yesmaximal, characteristic
6#11718611C211yesmaximal, characteristic
7#11718607C211yesmaximal, characteristic
8#11718603C211yesmaximal, characteristic
9C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
10C4×#6101C211yesmaximal, characteristic, complemented
11C4×#6101C211yesmaximal, characteristic, complemented
12#11718316C211yesmaximal, characteristic, complemented
13#11718315C211yesmaximal, characteristic, complemented
14#11718308C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C23×Dic13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C42×C13C2211yescharacteristic
23C2×C42×C13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×C4×Dic13—24no—
36C2×C4×Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41C2×C4×Dic13C2211yescharacteristic
42#88132C418yesdirect product factor
43C4×Dic26—24no—
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54C24×C13C2311yescharacteristic
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13Q814yescomplemented
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13C2×C414yes—
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C2×Dic26—22no—
79C2×Dic26—22no—
80C2×Dic26C2×C414yescomplemented
81C13×C22⋊C4—22no—
82C13×C22⋊C4C2×C414yes—
83C42×C13—22no—
84C42×C13—22no—
85C22⋊Dic13—22no—
86C22⋊Dic13C2×C414yes—
87C4⋊Dic13—22no—
88C4⋊Dic13—22no—
89C4⋊Dic13C2×C414yescomplemented
90#6101—22no—
91#6101—22no—
92#6101—22no—
93#6101—22no—
94#6101C2×C414yescomplemented
95#6101C2×C414yescomplemented
96C4×Dic13—22no—
97C4×Dic13—22no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13D414yes—
102C4×C22⋊Q8—131nomaximal, Sylow
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13C22×C412yes—
108C23×C13C2×Q812yes—
109C23×C13#4112yes—
110C23×C13C2411yescharacteristic
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—28no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13C22×C412yes—
125C2×C4×C13C22×C412yes—
126C2×C4×C13C2×D412yes—
127C2×C4×C13C2×Q812yes—
128C2×C4×C13C2×Q812yes—
129C2×C4×C13#4112yes—
130C2×Dic13—28no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—28no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13C22×C412yes—
149C2×Dic13C22×C412yes—
150C2×Dic13C22×C412yes—
151C2×Dic13C22×C412yes—
152C2×Dic13C2×D412yes—
153C2×Dic13C2×D412yes—
154C2×Dic13#4112yes—
155C2×Dic13#4112yes—
156Dic26—28no—
157C2×C22⋊Q8—131no—
158C2×C4×Q8—131no—
159C22×C42—131no—
160#391—131no—
161#389—131no—
162#387—131no—
163#387—131no—
164#385—131no—
165#385—131no—
166#380—131no—
167C4×C4⋊C4—131no—
168C4×C4⋊C4—131no—
169C4×C4⋊C4—131no—
170C4×C22⋊C4—131no—
171C4×C22⋊C4D1311yescharacteristic
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13C4×Q814yescomplemented
179C22×C13C23×C411yescharacteristic
180C22×C13C22×D411yescharacteristic
181C22×C13C22×Q811yescharacteristic
182C22×C13C2×#4111yescharacteristic
183C22×C13C2×#4111yescharacteristic
184C22×C13C2×#4111yescharacteristic
185C22×C13C2×#4111yescharacteristic
186C4×C13—22no—
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13C22⋊Q814yescomplemented
192Dic13—22no—
193Dic13—22no—
194Dic13—22no—
195Dic13—22no—
196Dic13—22no—
197Dic13—41no—
198Dic13—41no—
199Dic13C4×D414yes—
200C22×Q8—131no—
201C23×C4—131no—
202C23×C4—131no—
203C23×C4C2×D1311yescharacteristic
204C22⋊Q8—138no—
205C4×Q8—264no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C22⋊C4—131no—
216C2×C22⋊C4—131no—
217C2×C22⋊C4C2×D1311yescharacteristic
218C2×C22⋊C4C2×D1311yescharacteristic
219C2×C42—131no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—131no—
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—264no—
226C2×C42C2×D1311yescharacteristic
227C2×C42C2×D1311yescharacteristic
228#95—131no—
229#95—131no—
230#95—131no—
231#95—131no—
232#95—131no—
233#95—131no—
234#95—131no—
235#95—131no—
236#95C2×D1311yescharacteristic
237#95C2×D1311yescharacteristic
238C2×C13—24no—
239C2×C13C2×C4×D411yescharacteristic
240C2×C13C2×C4×Q811yescharacteristic
241C2×C13C4×#4111yescharacteristic
242C2×C13C2×C22⋊Q811yescharacteristic
243C2×C13#52511yescharacteristic
244C2×C13#52911yescharacteristic
245C2×C13#53311yescharacteristic
246C24C22×D1311yescharacteristic
247C2×Q8—134no—
248C2×Q8—262no—
249C2×Q8—262no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—131no—
253C22×C4—134no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4—262no—
264C22×C4—262no—
265C22×C4—262no—
266C22×C4Dic2614yescomplemented
267C22×C4C22×D1311yescharacteristic
268C22×C4C22×D1311yescharacteristic
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271C22×C4C22×D1311yescharacteristic
272C22×C4C22×D1311yescharacteristic
273C4⋊C4—134no—
274C4⋊C4—134no—
275C4⋊C4—134no—
276C4⋊C4—262no—
277C4⋊C4—262no—
278C4⋊C4—262no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C22⋊C4—22no—
283C22⋊C4—134no—
284C22⋊C4—262no—
285C22⋊C4C4×D1314yes—
286C42—22no—
287C42—22no—
288C42—134no—
289C42—262no—
290C42—262no—
291C42—262no—
292C42—262no—
293C42—262no—
294C13C4×C22⋊Q811yescharacteristic, complemented, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×Dic2612yes—
300C23C2×C4×D1312yes—
301C23#612712yes—
302C23C23×D1311yescharacteristic
303Q8—268no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—28no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—132no—
318C2×C4—132no—
319C2×C4—132no—
320C2×C4—132no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—132no—
324C2×C4—132no—
325C2×C4—268no—
326C2×C4—268no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4C2×Dic2612yes—
344C2×C4C2×Dic2612yes—
345C2×C4C2×C4×D1312yes—
346C2×C4C2×C4×D1312yes—
347C2×C4D4×D1312yes—
348C2×C4#612912yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22C4×Dic2614yescomplemented
356C22C22×Dic2611yescharacteristic
357C22C22×C4×D1311yescharacteristic
358C22C2×#612711yescharacteristic
359C22C2×D4×D1311yescharacteristic
360C22C2×#612911yescharacteristic
361C22#41×D1311yescharacteristic
362C22#41×D1311yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—134no—
369C4—262no—
370C4—262no—
371C4—262no—
372C4—262no—
373C4—262no—
374C4—521no—
375C4—521no—
376C4#8813214yesdirect product factor
377C2—24no—
378C2C2×C4×Dic2611yescharacteristic
379C2C2×#8813211yescharacteristic
380C2#1171922211yescharacteristic
381C2C4×#612911yescharacteristic
382C2#1171924311yescharacteristic
383C2C4×D4×D1311yescharacteristic
384C2#1171925211yescharacteristic
subgroupG/H
centerC22×C4C22×D13
commutatorC22×C13C23×C4
FrattiniC23C23×D13
FittingC4×C13×C22⋊C4C2
socle, cosocleC23×C13C24
prime radicalC24×C13C23
hypercenterC4×C22⋊C4D13
hypocenterC13C4×C22⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C4×Dic26C2semidirect
9. C4×C4⋊Dic13C2semidirect
10. C4×#6101C2semidirect
11. C4×#6101C2semidirect
12. #11718316C2semidirect
13. #11718315C2semidirect
14. #11718308C2semidirect
15. #11718307C2semidirect
42. #88132C4direct (N × H)
57. C22×C4×C13Q8semidirect
80. C2×Dic26C2×C4semidirect
89. C4⋊Dic13C2×C4semidirect
94. #6101C2×C4semidirect
95. #6101C2×C4semidirect
178. C22×C13C4×Q8semidirect
191. C4×C13C22⋊Q8semidirect
266. C22×C4Dic26semidirect
294. C13C4×C22⋊Q8semidirect
355. C22C4×Dic26semidirect
376. C4#88132direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4×Dic132
C2×#881322
C2×C4×Dic262
C4×C13×C22⋊C42
C4×C22⋊Dic132
#117186112
#117186072
#117186032
C4×C4⋊Dic132
C4×#61012
#117183162
#117183152
#117183082
#117183072
C4×C22⋊Q813